One Musician's Use of Combinations and Permutations

The study of combinations and permutations has fascinated scholars of all disciplines since ancient times. Within the seventeenth and eighteenth centuries, many music theorists used combinational and permutational techniques to arrange notes in to figures and motives in to phrases and periods, establishing an order of keys within a movement, and constructing entire movements (for example, by substituting motives or measures within a given section). Other extramusical tools used for the same purposes included arrangements of notes or motives according to the numbers generated by tossing dice, spinning a top, or random choice: